This may take up to 1 minute for every 3 scouts, so doing it with a group bigger than 15 scouts might get boring.

Everyone gathers in a circle, facing inward.
Leader starts by counting "1" or "1,2".
Next scout counts the next 1 or 2 numbers.
Everyone in sequence must say either 1 or 2 numbers.
Whoever is forced to say "10" is eliminated and the next scout starts counting again at "1".

The last scout is the winner.